I can't speak in detail to Einstein, but Newton's theories certainly contained simplifying assumptions, and the resulting small predictive errors, put scientists to work for centuries in an attempt to account for them. The assumptions [which bracketed the effects of the planets on each other, etc.] made the theory …
I can't speak in detail to Einstein, but Newton's theories certainly contained simplifying assumptions, and the resulting small predictive errors, put scientists to work for centuries in an attempt to account for them. The assumptions [which bracketed the effects of the planets on each other, etc.] made the theory both possible and fertile. That the spirit of Solow's provocative -- but also humorous -- opening statement; scientific theories are open-ended and subject to improvement because their setup makes them, in some sense, approximations. Darwin's made one big simplifying assumption, so big it's almost invisible, that evolution is a biological process, based on traits in individuals, but ever since Darwin scientists (especially social scientists) have asked whether selection could be group-based (today's "cultural evolution" researchers believe so), and it's a hot debate.
Galileo, though he was ignorant of algebra and statistics, asserted that mathematics is the "language of nature," and most scientists since have shared that assumption/assertion and have given it a deterministic spin -- to the extent that Einstein could not accept some of the non-deterministic implications of quantum theory, etc. Today, we have Stephen Wolfram -- a crank, perhaps, but an interesting one, suggesting that nature is a discrete and "computational" process rather than the law-bound mathematics-speaking entity described by Galileo. so, in the fields you describe I see lots of important, facilitative, fertile, but perhaps limiting assumptions.
Solow's "not quite true" was a joke at Milton Friedman's expense; yes, some of our assumptions may be unprovable, but we had better think our crucial assumptions make sense as statements about the world and are not just chosen to facilitate a result. Newton's assumption allowed him to focus on the main effect, which he had correctly identified, and what Solow proposes is completely in that spirit.
Thanks for the comment.
I can't speak in detail to Einstein, but Newton's theories certainly contained simplifying assumptions, and the resulting small predictive errors, put scientists to work for centuries in an attempt to account for them. The assumptions [which bracketed the effects of the planets on each other, etc.] made the theory both possible and fertile. That the spirit of Solow's provocative -- but also humorous -- opening statement; scientific theories are open-ended and subject to improvement because their setup makes them, in some sense, approximations. Darwin's made one big simplifying assumption, so big it's almost invisible, that evolution is a biological process, based on traits in individuals, but ever since Darwin scientists (especially social scientists) have asked whether selection could be group-based (today's "cultural evolution" researchers believe so), and it's a hot debate.
Galileo, though he was ignorant of algebra and statistics, asserted that mathematics is the "language of nature," and most scientists since have shared that assumption/assertion and have given it a deterministic spin -- to the extent that Einstein could not accept some of the non-deterministic implications of quantum theory, etc. Today, we have Stephen Wolfram -- a crank, perhaps, but an interesting one, suggesting that nature is a discrete and "computational" process rather than the law-bound mathematics-speaking entity described by Galileo. so, in the fields you describe I see lots of important, facilitative, fertile, but perhaps limiting assumptions.
Solow's "not quite true" was a joke at Milton Friedman's expense; yes, some of our assumptions may be unprovable, but we had better think our crucial assumptions make sense as statements about the world and are not just chosen to facilitate a result. Newton's assumption allowed him to focus on the main effect, which he had correctly identified, and what Solow proposes is completely in that spirit.